SOLUTION: find the equation of the line tangent to the ellipse x^2+3y^2-x+2y=0 at the origin

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Question 1024076: find the equation of the line tangent to the ellipse x^2+3y^2-x+2y=0 at the origin
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Since the tangent line to the ellipse passes through the origin, the line will have the form y = mx, where m is the slope of the line.
==> x%5E2%2B3%28mx%29%5E2-x%2B2mx=0, after substitution
==> %281%2B3m%5E2%29x%5E2%2B%282m-1%29x+=+0 after simplifying...
For tangency, the discriminant b%5E2+-+4ac+=+0
==> %282m-1%29%5E2+-+4%281%2B3m%5E2%29%280%29+=+0, or
%282m-1%29%5E2+=+0, or m = -1/2.
Therefore the line tangent to the ellipse at (0,0) is y = -x/2.